# Question

Consider independent trials, each of which results in outcome i, i = 0, 1, . . . , k, with probability pi,

Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome.

(a) Find P{N = n}, n ≥ 1.

(b) Find P{X = j}, j = 1, . . . , k.

(c) Show that P{N = n,X = j} = P{N = n}P{X = j}.

Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome.

(a) Find P{N = n}, n ≥ 1.

(b) Find P{X = j}, j = 1, . . . , k.

(c) Show that P{N = n,X = j} = P{N = n}P{X = j}.

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